Granger Causalityin fMRI connectivity analysis

Alard Roebroeck

Maastricht Brain Imaging Center (MBIC)Faculty of Psychology & Neuroscience

Maastricht University

Overview•fMRI signal & connectivity•Functional & Effective connectivity•Structural model & Dynamical model

–Identification & model selection•Granger causality & fMRI

–Granger causality and its variants–Granger causality mapping

• Issues with variable hemodynamics–Hemodynamic deconvolution

Integration and connectivity• Performance of complex

tasks requiresinteraction of specializedbrain systems(functional integration)

• Interaction of specializedareas requiresconnectivity

• Investigation of complextasks requiresconnectivity analysis

Brain

Brain

A problem for fMRIconnectivity

• In fMRI our access to theneural activity is indirect

• We want to inferinteraction between AreaX and Y fromobservations x[t] and y[t](time-series)

Hemo-dynamics

Hemo-dynamics

Hemo-dynamics

Hemo-dynamics

MRIscanner

MRIscanner

MRIscanner

MRIscanner

signal x[t]

signal y[t]

access

fMRI: The BOLD signal

Neural pathway Hemodynamics MR scanner

time [s]~0.5÷2 ~4 ~10

stimulus

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Stimulus

Overview•fMRI signal & connectivity•Functional & Effective connectivity•Structural model & Dynamical model

–Identification & model selection•Granger causality & fMRI

–Granger causality and its variants–Granger causality mapping

• Issues with variable hemodynamics–Hemodynamic deconvolution

Functional & EffectiveConnectivity

•Functional connectivity–Association (mutual information)–Localization of whole networks

•Effective connectivity–Uncover network mechanisms

(causal influence)–Directed vs. undirected–Direct vs. indirect

brain

measurement

data

Effective connectivity modeling

Inferredmodel

Structural model& priors Dynamical model& priors

Effective connectivity

Effective connectivity

• ROI selection• Graph selection

Structural model& priors

What interacts

Dynamical model& priors

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• Deterministic vs.stochastic models

• Linear vs. non-linear• Forward observation

models

How does it interact:signal model

Problem: spurious influence

• Danger of strong structural models:• When important regions are ‘left out’(of the

anatomical model), ANY correct method will give‘wrong’answers

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Overview•fMRI signal & connectivity•Functional & Effective connectivity•Structural model & Dynamical model

–Identification & model selection•Granger causality & fMRI

–Granger causality and its variants–Granger causality mapping

• Issues with variable hemodynamics–Hemodynamic deconvolution

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• Predictions are quantified with a linearmultivariate autoregressive (AR) model– Though not necessarily: non-linear AR or nonparametric

(e.g. Dhamala et al., NI, 2008)• AR Transfer function form gives frequency

distribution• Various normalizations

– Geweke’s decomposition (Geweke, 1982; Roebroeck, NI,2005)

– Directed transfer function (DTF; Blinowska, PhysRevE,2004; Deshpande, NI, 2008)

– Partial directed coherence (PDC; Sameshima,JNeuSciMeth, 1999; Sato, HBM, 2009)

Granger causality(G-causality)

Sampling & Hemodynamics

X Y ?

Granger causality analysis

Roebroeck, NI 2005

Structural model for GC•ROI-based as in SEM, DCM

–E.g. Stilla, 2007; Sridharan, 2008;Udaphay, 2008; Deshpande, 2008

•Massively multivariate based onparcelation of the cortex–Valdes Sosa, 2004, 2005

•Granger causality mapping–Massively bivariate without prior

anatomical asumptions

Granger causality mapping (GCM)

Roebroeck, NI 2005; Goebel, MRI 2004

Random effects level GCMs

Granger causality mapping (GCM)

Roebroeck, NI 2005; Goebel, MRI 2004

Experimental modulation:• Functional assignment• Avoid HRF confound

Overview•fMRI signal & connectivity•Functional & Effective connectivity•Structural model & Dynamical model

–Identification & model selection•Granger causality & fMRI

–Granger causality and its variants–Granger causality mapping

• Issues with variable hemodynamics–Hemodynamic deconvolution

Hemodynamics & GC

• GC could be due purely to differences inhemodynamic latencies in different partsof the brain

• Which are estimated to be in the order of100’s - 1000’s ms (Aguirre, NI, 1998;Saad, HBM, 2001)

Hemodynamics & GC

• Caution needed in applying and interpretingtemporal precedence

• Tools:– Finding experimental modulation of GC– Studying temporally integrated signals for slow processes

(e.g. fatigue; Deshpande, HBM, 2009)– Combining fMRI with EEG or MEG– Hemodynamic deconvolution

Hemodynamic deconvolution

• Deconvolve neuronal source signal s(t) andhemodynamic response h(t) from fMRI signal– E.g. by wiener deconvolution (Glover, NI, 1999)

• Only possible if:– Strong constraints on s(t) are assumed (e.g. DCM:

stimulus functions), or– An independent measure of s(t) is available (e.g.

simultaneous EEG) and EEG/fMRI coupling can be assumed

fMRI signal =

m(t) = s(t) h(t)

Hemodynamic deconvolution

Granger withoutdeconvolution Granger using deconvolutionDCM

•Rat study of epilepsy•Simultaneous fMRI/EEG

•Gold standard model =>

S1BF HRF

David, PLoS Biology, 2008

Summary

•G-causality and AR models arepowerful tools in fMRI effectiveconnectivity analysis

•GC is ideal for massive explorationof the structural model

•Caution is needed with GC in theface of variable hemodynamics